Quasar's powers are derived from the pair of quantum bands fused to his wrists (or more specifically, from the seven gems on each of the bands). They are linked to their wearer's nervous system and grant tremendous powers of energy manipulation.
Foremost amongst these powers is the ability to tap into a limitless energy source called the quantum zone. Quasar can project quantum energy in the form of devastating beams of force or heat, but more commonly employs them to fashion incredibly durable constructs of solid energy, such as containment spheres or pincers. He protects himself with a personal force field of quantum energy.
The quantum bands can also exert control over many other types of energy that are part of the electromagnetic spectrum. For example, Quasar once tapped into a sun and caused it to emit an enormous solar flare. He can also absorb and redirect the cosmic energy wielded by such powerful beings as the Silver Surfer, Jack of Hearts, Adam Warlock, Thanos, Phoenix, and the Watchers, siphoning their power and using it to augment his quantum energy. Forms of energy the quantum bands cannot control include magic and darkforce.
Although he cannot overtly affect psionic energy, Quasar has programmed his bands to render him impervious to psionic mental control. Even Moondragon and the Overmind proved unable to overcome this defense. He does not appear to be protected from magical forms of compulsion.
Quasar can create apertures into and out of the quantum zone, thus allowing passage through its infinite, featureless expanse. He mainly uses this ability to traverse interstellar distances in a manner similar to hyperspace travel. The effect is essentially a form of teleportation, which Quasar refers to as a quantum jump. A quantum jump has a destructive side effect on the local environment, violently upheaving gravity and tearing holes in the atmosphere (on Earth, it would damage the ozone layer), so Quasar initially refrained from using it except when in space or in dire circumstances. However, he eventually realized that he could contain this side effect by first surrounding himself with a barrier of solid energy. Quasar can also shunt other matter into the quantum zone provided that he's in physical contact with it.
The quantum bands enable their wearer to fly by manipulating gravitons. The maximum flight speed he can attain is unknown, but he made a trip from Earth to Uranus in approximately four years flying non-stop (this was before he learned how to quantum jump). That would require a constant speed of roughly 50,000 miles per hour. This doesn't take into account the velocity he can achieve in a short burst of acceleration.
The quantum band gems seem to be able to analyze and process information as if they were extremely advanced computers. This allows Quasar to navigate the quantum zone and the depths of space. The gems are able to detect, analyze, and track energy emissions across vast distances. They can also "program" his quantum energy to register and react to certain preset conditions. For instance, at one time Quasar had the Earth surrounded with an invisible laticework of energy that was designed to act as a global alert system against potential extraterrestrial threats. The energy field could detect any surges of exotic energy emanating from the planet's surface as well as if any object larger than a micrometeorite passed through it; in either case, the field would react by transmitting an alert signal to the quantum bands.
Quasar has a direct link to Epoch through his bands, which gives him ready access to her nascent omniscience.
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The Star Brand
While he possessed the power of the Star Brand, Quasar gained the abilities of flight, superhuman strength and resilience. He also was able to regenerate his entire body from minute remains and did not need to eat, drink, or breathe. However, virtually all of the energy derived from the Star Brand was depleted not long after he gave it away. The Living Tribunal later stated that Quasar's body retains only an insignificant trace amount of energy.
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Cosmic awareness
Quasar also briefly possessed the same powers of cosmic awareness that Eon granted to the origial Captain Marvel. By simply concentrating for a moment, he could gain complete knowledge about virtually anything in the universe. It's unclear why Eon didn't bestow cosmic awareness on Quasar permanently, but being nigh-omniscient himself, he likely determined that it would have been detrimental to Quasar's psyche (as it was to that of Genis-Vell). The fact that he received the awareness while his mind was inhabiting an energy construct, and he did not demonstrate it upon returning to his body, may also have something to do with it.
From the Wikipedia entry for Quasar
http://en.wikipedia.org/wiki/Quasar_(comics)